%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU652^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:58 AM UTC 2026
% Result : Theorem 1.59s 1.36s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 287 ( 85 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 334 ( 10 ~; 4 |; 14 &; 256 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 10 con; 0-2 aty)
% ( 24 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 85 ( 30 ^; 46 !; 9 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(f59,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f58,f53]) ).
thf(f53,plain,
sK1 != sK0,
inference(superposition,[status(thm)],[f21,f50]) ).
thf(f50,plain,
sK1 = sK2,
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( sK1 = sK2 )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f39,f46]) ).
thf(f46,plain,
( $true
= ( in @ sK2 @ ( setadjoin @ sK1 @ emptyset ) ) ),
inference(superposition,[status(thm)],[f43,f22]) ).
thf(f22,plain,
( ( setadjoin @ sK1 @ emptyset )
= ( setadjoin @ sK2 @ ( setadjoin @ sK0 @ emptyset ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( uniqinunit = $true )
& ( ( setadjoin @ sK1 @ emptyset )
= ( setadjoin @ sK2 @ ( setadjoin @ sK0 @ emptyset ) ) )
& ( sK0 != sK2 )
& ( setadjoinIL = $true )
& ( secondinupair = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
& ( X0 != X2 ) )
=> ( ( ( setadjoin @ sK1 @ emptyset )
= ( setadjoin @ sK2 @ ( setadjoin @ sK0 @ emptyset ) ) )
& ( sK0 != sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( uniqinunit = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
& ( X0 != X2 ) )
& ( setadjoinIL = $true )
& ( secondinupair = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
& ( X0 != X2 ) )
& ( secondinupair = $true )
& ( uniqinunit = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( setadjoinIL = $true )
=> ( ( uniqinunit = $true )
=> ( ( secondinupair = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( setadjoinIL
=> ( uniqinunit
=> ( secondinupair
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( setadjoinIL
=> ( uniqinunit
=> ( secondinupair
=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
=> ( X0 = X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( setadjoinIL
=> ( uniqinunit
=> ( secondinupair
=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VYPEFNwCMA/DTF2THF_12057.p',upairequniteq) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f25,f20]) ).
thf(f20,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f25,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VYPEFNwCMA/DTF2THF_12057.p',setadjoinIL) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( X2 = X1 ) )
| ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f26,f23]) ).
thf(f23,plain,
uniqinunit = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f26,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VYPEFNwCMA/DTF2THF_12057.p',uniqinunit) ).
thf(f21,plain,
sK0 != sK2,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f58,plain,
sK1 = sK0,
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( sK1 = sK0 )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f39,f54]) ).
thf(f54,plain,
( ( in @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= $true ),
inference(superposition,[status(thm)],[f33,f22]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f24,f19]) ).
thf(f19,plain,
secondinupair = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f24,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VYPEFNwCMA/DTF2THF_12057.p',secondinupair) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU652^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n027.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:29:52 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU652^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Ordered Pairs - Properties of Pairs
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! x:i.! y:i.! z:i.setadjoin x (setadjoin y emptyset) =
% 0.30/0.46 % setadjoin z emptyset -> x = y)
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC154l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.20 v5.3.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 3 def)
% 0.30/0.46 % Number of atoms : 15 ( 6 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 5 ( 3 avg)
% 0.30/0.46 % Number of connectives : 25 ( 0 ~; 0 |; 0 &; 20 @)
% 0.30/0.46 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 8 ( 3 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 7 ( 6 usr; 4 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=208
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset_type,type,
% 0.30/0.46 emptyset: $i ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin_type,type,
% 0.30/0.46 setadjoin: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIL_type,type,
% 0.30/0.46 setadjoinIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIL,definition,
% 0.30/0.46 ( setadjoinIL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(uniqinunit_type,type,
% 0.30/0.46 uniqinunit: $o ).
% 0.30/0.46
% 0.30/0.46 thf(uniqinunit,definition,
% 0.30/0.46 ( uniqinunit
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(secondinupair_type,type,
% 0.30/0.46 secondinupair: $o ).
% 0.30/0.46
% 0.30/0.46 thf(secondinupair,definition,
% 0.30/0.46 ( secondinupair
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairequniteq,conjecture,
% 0.30/0.46 ( setadjoinIL
% 0.30/0.46 => ( uniqinunit
% 0.30/0.46 => ( secondinupair
% 0.30/0.46 => ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.46 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 = ( setadjoin @ Xz @ emptyset ) )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.59/1.32 ---- Embedded in THF ---
% 1.59/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.59/1.32 %%% Generated on Tue Feb 24 12:29:53 EST 2026
% 1.59/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.59/1.32 %%% Logic specification used:
% 1.59/1.32 %%% thf(spec, logic, $$dhol).
% 1.59/1.32
% 1.59/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VYPEFNwCMA/DTF2DTF12057.p
% See solution above
% 1.59/1.32 ------------------------
% 1.59/1.34 ---- Cleaned THF ---
% 1.59/1.34 thf(in_type,type,
% 1.59/1.34 in: $i > $i > $o ).
% 1.59/1.34
% 1.59/1.34 thf(emptyset_type,type,
% 1.59/1.34 emptyset: $i ).
% 1.59/1.34
% 1.59/1.34 thf(setadjoin_type,type,
% 1.59/1.34 setadjoin: $i > $i > $i ).
% 1.59/1.34
% 1.59/1.34 thf(setadjoinIL_type,type,
% 1.59/1.34 setadjoinIL: $o ).
% 1.59/1.34
% 1.59/1.34 thf(setadjoinIL,definition,
% 1.59/1.34 ( setadjoinIL
% 1.59/1.34 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.59/1.34
% 1.59/1.34 thf(uniqinunit_type,type,
% 1.59/1.34 uniqinunit: $o ).
% 1.59/1.34
% 1.59/1.34 thf(uniqinunit,definition,
% 1.59/1.34 ( uniqinunit
% 1.59/1.34 = ( ! [Xx: $i,Xy: $i] :
% 1.59/1.34 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.59/1.34 => ( Xx = Xy ) ) ) ) ).
% 1.59/1.34
% 1.59/1.34 thf(secondinupair_type,type,
% 1.59/1.34 secondinupair: $o ).
% 1.59/1.34
% 1.59/1.34 thf(secondinupair,definition,
% 1.59/1.34 ( secondinupair
% 1.59/1.34 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.59/1.34
% 1.59/1.34 thf(upairequniteq,conjecture,
% 1.59/1.34 ( setadjoinIL
% 1.59/1.34 => ( uniqinunit
% 1.59/1.34 => ( secondinupair
% 1.59/1.34 => ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.59/1.34 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.59/1.34 = ( setadjoin @ Xz @ emptyset ) )
% 1.59/1.34 => ( Xx = Xy ) ) ) ) ) ).
% 1.59/1.34 ------------------------
% 1.59/1.35 % (12248)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12057 for (2999ds/183Mi)
% 1.59/1.35 % (12248)First to succeed.
% 1.59/1.36 % (12248)Refutation found. Thanks to Tanya!
% 1.59/1.36 % SZS status Theorem for DTF2THF_12057
% 1.59/1.36 % SZS output start Proof for DTF2THF_12057
% 1.59/1.36 thf(func_def_0, type, in: $i > $i > $o).
% 1.59/1.36 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.59/1.36 thf(f59,plain,(
% 1.59/1.36 $false),
% 1.59/1.36 inference(subsumption_resolution,[status(thm)],[f58,f53])).
% 1.59/1.36 thf(f53,plain,(
% 1.59/1.36 (sK1 != sK0)),
% 1.59/1.36 inference(superposition,[status(thm)],[f21,f50])).
% 1.59/1.36 thf(f50,plain,(
% 1.59/1.36 (sK1 = sK2)),
% 1.59/1.36 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.59/1.36 thf(f48,plain,(
% 1.59/1.36 (sK1 = sK2) | ($true = $false)),
% 1.59/1.36 inference(superposition,[status(thm)],[f39,f46])).
% 1.59/1.36 thf(f46,plain,(
% 1.59/1.36 ($true = (in @ sK2 @ (setadjoin @ sK1 @ emptyset)))),
% 1.59/1.36 inference(superposition,[status(thm)],[f43,f22])).
% 1.59/1.36 thf(f22,plain,(
% 1.59/1.36 ((setadjoin @ sK1 @ emptyset) = (setadjoin @ sK2 @ (setadjoin @ sK0 @ emptyset)))),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f18])).
% 1.59/1.36 thf(f18,plain,(
% 1.59/1.36 (uniqinunit = $true) & (((setadjoin @ sK1 @ emptyset) = (setadjoin @ sK2 @ (setadjoin @ sK0 @ emptyset))) & (sK0 != sK2)) & (setadjoinIL = $true) & (secondinupair = $true)),
% 1.59/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f17])).
% 1.59/1.36 thf(f17,plain,(
% 1.59/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) & (X0 != X2)) => (((setadjoin @ sK1 @ emptyset) = (setadjoin @ sK2 @ (setadjoin @ sK0 @ emptyset))) & (sK0 != sK2))),
% 1.59/1.36 introduced(definition,[],[choice_axiom])).
% 1.59/1.36 thf(f16,plain,(
% 1.59/1.36 (uniqinunit = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) & (X0 != X2)) & (setadjoinIL = $true) & (secondinupair = $true)),
% 1.59/1.36 inference(flattening,[status(thm)],[f15])).
% 1.59/1.36 thf(f15,plain,(
% 1.59/1.36 ((? [X0 : $i,X1 : $i,X2 : $i] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) & (X0 != X2)) & (secondinupair = $true)) & (uniqinunit = $true)) & (setadjoinIL = $true)),
% 1.59/1.36 inference(ennf_transformation,[status(thm)],[f10])).
% 1.59/1.36 thf(f10,plain,(
% 1.59/1.36 ~((setadjoinIL = $true) => ((uniqinunit = $true) => ((secondinupair = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) => (X0 = X2)))))),
% 1.59/1.36 inference(fool_elimination,[status(thm)],[f9])).
% 1.59/1.36 thf(f9,plain,(
% 1.59/1.36 ~(setadjoinIL => (uniqinunit => (secondinupair => ! [X0 : $i,X1 : $i,X2 : $i] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) => (X0 = X2)))))),
% 1.59/1.36 inference(rectify,[status(thm)],[f5])).
% 1.59/1.36 thf(f5,negated_conjecture,(
% 1.59/1.36 ~(setadjoinIL => (uniqinunit => (secondinupair => ! [X1 : $i,X2 : $i,X0 : $i] : (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) = (setadjoin @ X2 @ emptyset)) => (X0 = X1)))))),
% 1.59/1.36 inference(negated_conjecture,[status(cth)],[f4])).
% 1.59/1.36 thf(f4,conjecture,(
% 1.59/1.36 setadjoinIL => (uniqinunit => (secondinupair => ! [X1 : $i,X2 : $i,X0 : $i] : (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) = (setadjoin @ X2 @ emptyset)) => (X0 = X1))))),
% 1.59/1.36 file('/export/starexec/sandbox/tmp/tmp.VYPEFNwCMA/DTF2THF_12057.p',upairequniteq)).
% 1.59/1.36 thf(f43,plain,(
% 1.59/1.36 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (setadjoin @ X2 @ X1)) = $true)) )),
% 1.59/1.36 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.59/1.36 thf(f42,plain,(
% 1.59/1.36 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1))) @ X2))) )),
% 1.59/1.36 inference(pi_clausification,[status(thm)],[f41])).
% 1.59/1.36 thf(f41,plain,(
% 1.59/1.36 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1)))))) )),
% 1.59/1.36 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.59/1.36 thf(f40,plain,(
% 1.59/1.36 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))) @ X1))) )),
% 1.59/1.36 inference(pi_clausification,[status(thm)],[f28])).
% 1.59/1.36 thf(f28,plain,(
% 1.59/1.36 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 1.59/1.36 inference(definition_unfolding,[status(thm)],[f25,f20])).
% 1.59/1.36 thf(f20,plain,(
% 1.59/1.36 (setadjoinIL = $true)),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f18])).
% 1.59/1.36 thf(f25,plain,(
% 1.59/1.36 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f12])).
% 1.59/1.36 thf(f12,plain,(
% 1.59/1.36 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 1.59/1.36 inference(fool_elimination,[status(thm)],[f11])).
% 1.59/1.36 thf(f11,plain,(
% 1.59/1.36 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 1.59/1.36 inference(rectify,[status(thm)],[f1])).
% 1.59/1.36 thf(f1,axiom,(
% 1.59/1.36 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 1.59/1.36 file('/export/starexec/sandbox/tmp/tmp.VYPEFNwCMA/DTF2THF_12057.p',setadjoinIL)).
% 1.59/1.36 thf(f39,plain,(
% 1.59/1.36 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X2 @ (setadjoin @ X1 @ emptyset))) | (X1 = X2)) )),
% 1.59/1.36 inference(equality_proxy_clausification,[status(thm)],[f38])).
% 1.59/1.36 thf(f38,plain,(
% 1.59/1.36 ( ! [X2 : $i,X1 : $i] : (($true = (X2 = X1)) | ($false = (in @ X2 @ (setadjoin @ X1 @ emptyset)))) )),
% 1.59/1.36 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.59/1.36 thf(f37,plain,(
% 1.59/1.36 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X2 @ (setadjoin @ X1 @ emptyset)) => (X2 = X1)))) )),
% 1.59/1.36 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.59/1.36 thf(f36,plain,(
% 1.59/1.36 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1))) @ X2))) )),
% 1.59/1.36 inference(pi_clausification,[status(thm)],[f35])).
% 1.59/1.36 thf(f35,plain,(
% 1.59/1.36 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1)))))) )),
% 1.59/1.36 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.59/1.36 thf(f34,plain,(
% 1.59/1.36 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0))))) @ X1))) )),
% 1.59/1.36 inference(pi_clausification,[status(thm)],[f29])).
% 1.59/1.36 thf(f29,plain,(
% 1.59/1.36 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 1.59/1.36 inference(definition_unfolding,[status(thm)],[f26,f23])).
% 1.59/1.36 thf(f23,plain,(
% 1.59/1.36 (uniqinunit = $true)),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f18])).
% 1.59/1.36 thf(f26,plain,(
% 1.59/1.36 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f14])).
% 1.59/1.36 thf(f14,plain,(
% 1.59/1.36 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 1.59/1.36 inference(fool_elimination,[status(thm)],[f13])).
% 1.59/1.36 thf(f13,plain,(
% 1.59/1.36 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 1.59/1.36 inference(rectify,[status(thm)],[f2])).
% 1.59/1.36 thf(f2,axiom,(
% 1.59/1.36 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 1.59/1.36 file('/export/starexec/sandbox/tmp/tmp.VYPEFNwCMA/DTF2THF_12057.p',uniqinunit)).
% 1.59/1.36 thf(f21,plain,(
% 1.59/1.36 (sK0 != sK2)),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f18])).
% 1.59/1.36 thf(f58,plain,(
% 1.59/1.36 (sK1 = sK0)),
% 1.59/1.36 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.59/1.36 thf(f56,plain,(
% 1.59/1.36 (sK1 = sK0) | ($true = $false)),
% 1.59/1.36 inference(superposition,[status(thm)],[f39,f54])).
% 1.59/1.36 thf(f54,plain,(
% 1.59/1.36 ((in @ sK0 @ (setadjoin @ sK1 @ emptyset)) = $true)),
% 1.59/1.36 inference(superposition,[status(thm)],[f33,f22])).
% 1.59/1.36 thf(f33,plain,(
% 1.59/1.36 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset))))) )),
% 1.59/1.36 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.59/1.36 thf(f32,plain,(
% 1.59/1.36 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (in @ X1 @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)))) @ X2))) )),
% 1.59/1.36 inference(pi_clausification,[status(thm)],[f31])).
% 1.59/1.36 thf(f31,plain,(
% 1.59/1.36 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ X1 @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset))))))) )),
% 1.59/1.36 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.59/1.36 thf(f30,plain,(
% 1.59/1.36 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))) @ X1))) )),
% 1.59/1.36 inference(pi_clausification,[status(thm)],[f27])).
% 1.59/1.36 thf(f27,plain,(
% 1.59/1.36 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 1.59/1.36 inference(definition_unfolding,[status(thm)],[f24,f19])).
% 1.59/1.36 thf(f19,plain,(
% 1.59/1.36 (secondinupair = $true)),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f18])).
% 1.59/1.36 thf(f24,plain,(
% 1.59/1.36 (secondinupair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f8])).
% 1.59/1.36 thf(f8,plain,(
% 1.59/1.36 (secondinupair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 1.59/1.36 inference(fool_elimination,[status(thm)],[f7])).
% 1.59/1.36 thf(f7,plain,(
% 1.59/1.36 (secondinupair = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 1.59/1.36 inference(rectify,[status(thm)],[f3])).
% 1.59/1.36 thf(f3,axiom,(
% 1.59/1.36 (secondinupair = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 1.59/1.36 file('/export/starexec/sandbox/tmp/tmp.VYPEFNwCMA/DTF2THF_12057.p',secondinupair)).
% 1.59/1.36 % SZS output end Proof for DTF2THF_12057
% 1.59/1.36 % (12248)------------------------------
% 1.59/1.36 % (12248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (12248)Termination reason: Refutation
% 1.59/1.36
% 1.59/1.36 % (12248)Memory used [KB]: 5500
% 1.59/1.36 % (12248)Time elapsed: 0.004 s
% 1.59/1.36 % (12248)Instructions burned: 4 (million)
% 1.59/1.36 % (12248)------------------------------
% 1.59/1.36 % (12248)------------------------------
% 1.59/1.36 % (12247)Success in time 0.015 s
%------------------------------------------------------------------------------